I understand that if I have two models A and B and A is nested in B then, given some data, I can fit the parameters of A and B using MLE and apply the generalized log likelihood ratio test. In particular, the distribution of the test should be $\chi^2$ with $n$ degrees of freedom where $n$ is the difference in the number of parameters that $A$ and $B$ have.
However, what happens if $A$ and $B$ have the same number of parameters but the models are not nested? That is they are simply different models. Is there any way to apply a likelihood ratio test or can one do something else?